There is a page summarizing the eligibility of people for EI.
You may be entitled to EI regular benefits if you:
Were employed in insurable employment
lost your job through no fault of your own
have been without work and without pay for at least seven consecutive days in the last 52 weeks
have worked for the required number of insurable employment hours in the last 52 weeks or since the start of your last EI claim, whichever is shorter
are ready, willing and capable of working each day
are actively looking for work
You may not be eligible if you left your work voluntarily.
It is normal that you can't claim if you quit, but if you were let go you can (with exceptions). Being on probation doesn't make any difference. You can be denied EI if you were fired for something that was your fault, such as gross misconduct, but you are not usually denied if you were fired for not being good enough at your job.
There is some discretion in whether you are given EI or not, so nobody can be 100% that you will get it or not in unusual cases.